Sensor array systems generally include multiple sensors arranged in an array such that each of the sensors measures a physical quantity generated by one or more emitting sources and converts the physical quantity into a representative signal. The representative signal generated by each sensor is often an analog signal (e.g., an RF signal) representative of the physical quantity measured by the sensors. To acquire sensor data for processing, the analog sensor signals may be demodulated to a baseband frequency (e.g., using RF demodulation) and converted to digital signals. By acquiring data from an array of sensors, a sensor array system may be used to determine information about a signal of interest, such as a direction-of-arrival, and about the source, such as the location.
In existing sensor array systems, parallel acquisition hardware is often used for each sensor in the array. Following each sensor, an existing sensor array system may include, for example, an analog RF chain composed of filters and mixers used to demodulate the received signal and an analog-to-digital converter (ADC) to sample each of the demodulated analog signals. Because these components perform the same functions for each sensor, this parallel acquisition hardware results in a redundant bank of complex components, which may be expensive and power intensive. Additionally, the amount of collected data grows linearly with the number of sensors in a sensor array system with redundant data acquisition hardware. In other words, for Nk sensors, there is Nk times more digital sensor data than with a single sensor and receiver. Increasing the number of sensors in such a system may thus require larger storage, higher transmission data rates and faster processing capabilities.
The spatial resolution of a sensor array may be dependent on the size of its aperture, and for a fixed sensor spacing, the number of sensors. Applications for sensor arrays have demanded higher spatial resolutions and thus an increased number of sensors, which results in more complex array acquisition hardware and larger amounts of data. In many applications, there are only a few emitting sources of interest. A sensor array may be used, for example, to look for the direction from which a single source is emitting. Although increasing the number of sensors in an array produces higher precision results with regard to the direction of the source, it comes at the cost of acquiring high resolution information about all of the other directions that do not contain the signal of interest. Thus, a system with more complex hardware is used to acquire more samples than are needed. Reducing the bottleneck created by the parallel acquisition hardware in existing sensor array systems would be advantageous in such systems.
Compressive sampling techniques have been applied to reduce the number of samples required to represent certain types of signals. According to the Shannon sampling theorem, a bandlimited signal can be uniquely represented by uniform time-samples if it is sampled at the Nyquist rate (twice the bandwidth) or faster. In existing sensor array systems with parallel acquisition hardware, each of the parallel ADCs often sample the sensor signals at the Nyquist rate determined by the bandwidth of the channel that each sensor receives. According to compressive sampling theory, a large class of signals known as sparse signals may be sampled significantly more efficiently than Shannon's theorem implies. A sparse signal is generally known as a signal that can be compactly or efficiently represented by a relatively small number of basis functions (e.g., nonzero coefficients) in some basis (e.g., time, frequency, wavelet, etc.). Many communications signals, for example, are composed of just a few sinusoids and thus may be represented by just a few nonzero coefficients in the Fourier domain. Compressive sampling techniques have been used to obtain the nonzero coefficients with much fewer samples than sampling at the Nyquist rate. Merely using compressive sampling in each of the ADCs of an existing sensor array system, however, does not eliminate the redundant acquisition hardware in sensor arrays.